I don't know much other than positive hearsay about the Honda inverter generators, but I do know something about their olive-drab cousins, the US Army "quiet" diesel gen sets. Frankly, they're ideal for variable load situations. The engine can run in something like a sweet spot for that load requirement which minimizes fuel consumption and noise, (Uncle Sugar likes them because they are very quiet under partial load) and the electronics do all the tweaking to get a constant 120 V sine wave output.
Problems? Well, if you're scared of potted electronics they're probably not an ideal solution. A properly-engineered one will do just fine as long as it has plenty of cooling air flow over the heat sinks. And yes, you should be able to integrate them easily into some sort of battery load-bank arrangement.